*A tree that is 16 feet tall is growing at a rate of 2 feet each year. A tree that is 6 feet tall is growing at a rate of 3 feet each year.
* Enter the number of years it will take the two trees to reach the same height.
Answers
Using Linear equations, It will take 10 years for the two trees to reach the same height.
Linear equation:The concept used in this problem is the Linear equation and solving for an unknown variable. Let us assume the number of years with the variable 'x' and form two linear equations according to the given condition. Now solve both equations for the value of 'x' and find the number of years.
Here we have
A tree that is 16 feet tall is growing at a rate of 2 feet each year.
A tree that is 6 feet tall is growing at a rate of 3 feet each year.
Let both trees reach the same height after 'x' years
The height of first tree= [ 16 + 2(x) ]
The height of the second tree = [ 6 + 3(x) ]
As we assumed both sides are equal
=> [ 16 + 2(x) ] = [ 6 + 3(x) ]
=> 16 + 2x = 6 + 3x
Subtract 6 from both sides
=> 6 - 6 + 3x = 16 - 6 + 2x
=> 3x = 10 + 2x
Subtract 2x from both sides
=> 3x - 2x = 10
=> x = 10
Therefore,
It will take 10 years for the two trees to reach the same height.
Learn more about Linear Equations at
https://brainly.com/question/29276464
#SPJ1
Related Questions
Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote:
228=2⋅28=56
Elena said, “No, exponents mean repeated multiplication. It should be 28⋅28, which works out to be 784.” Do you agree with either of them? Explain your reasoning.
Answers
Answer:
no, exponents are how many times the base is used, it would be 2x2x2... so on until there are 28 2s
Step-by-step explanation:
Orbital Toys sells two types of sets of magnetic spheres, silver and brass. The store owner, Lucy Ball, pays $8 and $16 for each one set of silver magnetic spheres and brass magnetic spheres respectively. One set of silver magnetic spheres yields a profit of $3 while a set of brass magnetic spheres yields a profit of $5. Ms. Ball estimates that no more than 2000 sets of magnetic spheres will be sold every month and she does not plan to invest more than $20,000 in inventory of these sets. How many sets of each type of magnetic spheres should be stocked in order to maximize her total monthly profit? What is her maximum monthly profit?
Answers
Answer:
The maximum profit will be reached by buying 500 brass magnetic spheres and 1500 silver magnetic spheres.
Step-by-step explanation:
In order to solve this you need to create a system of equations, with two values that will create the answer we are looking for, the thing that we don't know here is how many of each are we buying so the number of silver magnetic spheres will be represented by "y" and the brass magnetic spheres will be represented by "x".
So we know that x+y=2000
That's our first equation, our second would be the expense, which would be
8x+16y=20,000
We now just solve for one of them
x=(2000-y)
8(2000-y)+16y=20,000
16,000-8y+16y=20,000
8y=4,000
y=500
So we know that the maximum profit will be reached by buying 500 brass magnetic spheres and 1500 silver magnetic spheres.
Four different paints are advertised as having the same drying time. To check the manufacturer's claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.
Excel or Minitab users: The data set is available in file namedPaint.
Paint 1 Paint 2 Paint 3 Paint 4
128 144 133 150
137 133 143 142
135 142 137 135
124 146 136 140
141 130 132 153
At the = .05 level of significance, test to see whether the mean drying time is the same for each type of paint. Compute the values identified below:
1. Sum of Squares,Treatment
2. Sum of Squares,Error
3. Mean Squares,Treatment
4. Mean Squares,Error
Answers
Answer:
(1) 330
(2) 692
(3) 110
(4) 43.25
Step-by-step explanation:
The data provided is for the dying time of four different types of paint.
One-way ANOVA can be used to determine whether all the four paints have the same drying time.
Use Excel to perform the one-way ANOVA.
Go to Data → Data Analysis → Anova: Single Factor
A dialog box will open.
Select the data.
Select "Grouping" as Columns.
Press OK.
The output is attached below.
The required values are as follows:
(1)
Sum of Squares of Treatment (Between Subjects):
SST = 330
(2)
Sum of Squares of Error (Within Subjects):
SSE = 692
(3)
Mean Squares Treatment (Between Subjects):
MST = 110
(4)
Mean Squares Error (Within Subjects):
MSE = 43.25
If the diameter of a circle is 10 inches, what is the area of a circle?
Answers
Answer:
25\(\pi\)
Step-by-step explanation:
because area is pi r^2
Answer:
78.54 or 25π (if in terms of pi)
Step-by-step explanation:
A = πr² = π*5² ≈ 78.53982
how do find the domain and range from a graph, and writing it as an inequality
Answers
To determine the range is the same as to determine which numbers appear as the second number (the y-value) in an ordered pair that is part of the graph.
Here are some examples:
y
≥
x
2
+
3
graph{y >= x^2+3 [-11.6, 13.72, 0.15, 12.81]}
Although it is not 100% certain from just the graph, this graph does get wider and wider. Every
x
does appear in some ordered pair on the graph. The domain is all real numbers.
The
y
values that appear start at
3
and go up. We get all numbers greater than or equal to
3
. Inequality:
y
≥
3
.
If you've learned interval notation, you write:
[
3
,
∞
)
x
2
+
y
2
9
≤
1
# graph{x^2 + y^2/9 <= 1 [-5.35, 7.14, -3.105, 3.14]}
Domain (x-values) Go from
−
1
to
1
(inequality:
−
1
≤
x
≤
1
)(interval:
[
−
1
,
1
]
)
Range:
−
3
to
3
(inequal:
−
3
≤
y
≤
3
(interval:
[
−
3
,
3
]
)
More challenging:
x
2
+
y
2
<
9
graph{x^2+y^2 < 9 [-5.35, 7.14, -3.105, 3.14]}
The dotted line is not included, so we do not include the points at
−
3
or at
3
.
Domain:
−
3
<
x
<
3
(interval
(
−
3
,
3
)
)
R
a
n
≥
:
-3(
∫
e
r
v
a
l
(-3, 3))
Last one:
x
−
y
2
<
6
graph{x- y^2 < 6 [-9.87, 30.68, -9.96, 10.32]}
Domain: all real numbers
Range: all real numbers
A tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. Approximately how much canvas would be needed to cover the tepee?
Answers
To find:
The area of canvas needed to cover the tepee.
Solution:
Given that the tepee is in the shape of a right cone, with slant height 18.5 feet and diameter of 20 feet then the radius is 10 feet.
The area of canvas is equal to the curved surface area of the tepee. It is known that the curve surface area of the cone is given by:
\(CSA=\pi rl\)Where, r is the radius of the cone and l is the slant height of the cone. So,
\(\begin{gathered} CSA=3.14\times10\times18.5 \\ =580.9ft^2 \end{gathered}\)Thus, the approximate canvas that would be needed to cover the tepee is 580.9 ft^2.
581Answer:
Step-by-step explanation:
2. Claire drinks 64 fluid ounces of water o day. How many gallons of water does she drink in a week?
Answers
Answer:
3.5 gallons a week
Step-by-step explanation:
Well 64 gl Oz is basically half a gallon. So half a gallon of water a day would result in 0.5*7 (7 days in a week) and you would get 3.5 gallons.
2/10 x 1/9 = 2/90 = 1/?
Answers
Answer: 2/90 = 1/45
Step-by-step explanation:
when factoring 6x^2 -7x-20 by grouping , how should the middle term be rewritten
Answers
Answer: -7x should be written as -15x+8x or 8x-15x
===============================================
Explanation:
Multiply the first coefficient 6 and the last term -20 to get -120
We need to find factors of -120 that add to the middle coefficient -7
Through trial and error you should find that
-15 + 8 = -7
-15 * 8 = -120
Therefore, we break the -7x into -15x+8x
----------------------------
Extra info: if you want to fully factor by grouping, then follow these steps
6x^2 - 7x - 20
6x^2 - 15x + 8x - 20 ... break up -7x
(6x^2 - 15x) + (8x - 20) .... group into pairs
3x(2x - 5) + 4(2x - 5) .... factor each group
(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5
So 6x^2-7x-20 fully factors to (3x+4)(2x-5)
We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.
Find the measure of the missing angle.
A=
(answer is in degrees)
Answers
Answer:
Right angles is 90° so 90°+30°=120°.A straight line is 180°. So you do 180°-120° which is 60. So A=60°
Keegan is determining whether the triangle with vertices L(-1, 3), M(5, 5) and N(7, -1) is a right triangle. Keegan finds the slopes as shown and concludes that the triangle is not a right triangle because the product is not -1. What is his error and what should he do to correct it?
(added an image)
will mark brainiliest
Answers
Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.
To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.
If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
Find the perimeter of the triangle and put your answer in the simplest radical form:
Answers
Answer:
\(14\sqrt[4]{5}+2\sqrt[3]{3}\)
Step-by-step explanation:
\(3\sqrt[4]{80}+\sqrt[3]{24}+8\sqrt[4]{5}\\=3\sqrt[4]{16*5}+\sqrt[3]{8*3}+8\sqrt[4]{5}\\=(3*2)\sqrt[4]{5}+2\sqrt[3]{3}+8\sqrt[4]{5}\\=6\sqrt[4]{5}+2\sqrt[3]{3}+8\sqrt[4]{5}\\=14\sqrt[4]{5}+2\sqrt[3]{3}\)
Label the triangle sides, assuming the angle of interest is the 30-degree angle:
solve for
The side with x is the
blank side.
The side with y is the
NO SPAM I WILL REPORT YOU
blank side.
The side with 17 is the blank side
Answers
Check the picture below.
In 1/6 of a day Bart read 4/7 of comic book .what rate can he read in a day
Answers
The rate at which Bart read is 24/7 book/day.
Given, Bart read 4/7 of comic book in 1/6 of a day.
We have to find the rate at which he read the book in a day.
Now, Bart read 4/7th of a comic book = 1/6th of a day
4/7 comic book = 1/6 day
1 day = (4 × 6)/7 comic book
1 day = 24/7 comic book
So, the rate at which Bart read is 24/7 book/day.
Hence, the rate at which Bart read is 24/7 book/day.
Learn more about Unitary Method here https://brainly.com/question/28627316
#SPJ1
HELP ITS DUE TMR PLEASE
Answers
Answer:
im pretty sure the answer is (-5,-7)?
Triangle PQR has vertives P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up to produce Triangle P'Q'R'. Complete table.
Answers
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
What are the locations of the vertices of the triangle after applying rigid transformations?
In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting point T(x, y) - Translation vectorIf we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:
P'(x, y) = (2, - 4) + (- 6, 3)
P'(x, y) = (- 4, - 1)
Q'(x, y) = (4, - 5) + (- 6, 3)
Q'(x, y) = (- 2, - 2)
R'(x, y) = (7, - 2) + (- 6, 3)
R'(x, y) = (1, 1)
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
To learn more on rigid transformations: https://brainly.com/question/1761538
#SPJ1
Find non-invertible matrices A,B such that A+B is invertible. Choose A,B so that (1) neither is a diagonal matrix and (2) A,B are not scalar multiples of each other.A = [_____ _____][_____ _____]B = [_____ _____][_____ _____]
Answers
Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:
Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is
\(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\)
Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
\(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\)
Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:
\(A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\)
Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:
det(A+B) = (1)(1) - (1)(1) = 0
Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.
Therefore, the matrices \(A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]\) and \(B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right]\) are non-invertible matrices that can be added together to form an invertible matrix \(A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]\).
https://brainly.in/question/8463680
#SPJ1
Which region represents the solution to the given system of inequalities?
A
B
C
D
Answers
Which graph represents 12 = 3x + 4y line a, line b, line c
Answers
Answer:
green line or "b"
Step-by-step explanation:
we can set this up into the slope intercept form
y=mx+b
where m is the slope and b is y intercept
12=3x+4y
-3x -3x
-3x+12=4y
/4. /4. /4
-3/4x+3=y
we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"
hopes this helps please mark rainliest
777×900
Can u help me
Answers
1st Answer:
The answer to this would be 699,300!
Have a great day good luck! Plugging it into a calculator was easy^^
Answer:
699,300
Step-by-step explanation:
777x900=699,300
What is the area of the region of points
satisfying the inequalities x ≤ 0, y ≤ 0, and
y ≥ |x + 4| − 5?
Answers
the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.
PLEASE HELP FAST!! WILL GET BRAINLIEST
Answers
Relation between these given lines are given as follows:
A is parallel to ED is perpendicular to FE is a horizontal lineC is a verticle lineB is perpendicular to DWhat are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given a graph, there are a few lines in the graph we need to find the relation between them.
Since there is no mathematical data we need to observe the lines as per the graph
Since we already know about parallel and perpendicular.
So, Horizontal and verticle lines are:
A vertical line is a line, parallel to the y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to the x-axis and goes straight, left, and right.
Therefore, Relation between these given lines are given as follows:
A is parallel to ED is perpendicular to FE is a horizontal lineC is a verticle lineB is perpendicular to DLearn more about parallel lines here:
https://brainly.com/question/28969931
#SPJ1
Jamison wants to save up his money to buy a car. His parents said they will match what he saves, up to $2000. Jamison mows lawns in the summer, and shovels snow in the winter. He charges $25 per lawn, and $20 per driveway. Let X represent the amount of money that Jamison can save so that his parents will match the amount. Let L represent the number of lawns he mows , and T represent the number of driveways he shovels. Which of the following inequalities need to be part of the system? Select all that apply.
25L + 20d < x
x (greater than or equal to) 2000
20L+25d=x
25L+20d=x
x(less that or equal to)2000
Answers
Answer:
25l+20d=x and x ≤ 2000 needs to be part of the system.
Step-by-step explanation:
Given that:
Amount charged per lawn = $25
Number of lawns = l
Amount charged per driveway = $20
Number of driveways = d
Amount saved by Jamison = x
\(25l+20d=x\)
Amount given by parents = upto $2000
It means the parents will not give more money than $2000, therefore, we will use less than equal to inequality
x ≤ 2000
Hence,
25l+20d=x and x ≤ 2000 needs to be part of the system.
Anton needs to buy 3.5 meters of cloth for their project in TLE. If 1 meter of cloth costs P35.00, how much will he spend for 3.5 meters of cloth? a. What is asked in the problem? b. What are the given facts? c. What operation will be used? d. What is the nunber sentence? e. What is the answer?
Answers
Answer:
The correct answer is -
a. Amount Anton will spend for 3.5 m of cloth
b. 3.5 meters of cloth, 35.00 costs per meter.
c. Multiplication
d. 35.00 × 3.5/1 = N
e. P122.50 amount he will spend for 3.5 meters of cloth
Step-by-step explanation:
Solution:
A. in this question it is asked that how much it will cost Anton to buy the required cloth that is 3.5 meters cloth.
B. Given:
required cloth - 3.5 meters
price or cost of cloth per meter - 35 per meter
C. In this question multiplication will be used to get the answer so the operation would be - multiplication.
D. The number sentence is an equation to express inequality by using numbers and mathematical symbols, here the number sentence would be -
35.00 × 3.5/1 = N
E. The correct answer would be -
N = 35.00 × 3.5/1
= 122.5
Thus, the correct answer would be P 122.5.
helppppppppppppppppppppp
Answers
Answer:
75%
Step-by-step explanation:
450/600 = 0.75
0.75 as a percent is 75%
hope this helps:)
Answer:
75%
Step-by-step explanation:
Write an equation for the line having slope -6 that passes through the
point (5,-5).
Answers
Answer:
An equation for the statement is y = -6x + 25.
What is the solution to x2 – 9x < –18? ASAP will give brainliest
x < –6 or x > 3
–6 < x < 3
x < 3 or x > 6
3 < x < 6
Answers
The solution to the inequality equation \(x^{2}\) – 9x < –18 is 3 < X < 6
Inequality equationInequality equation means a mathematical expression in which the sides are not equal to each other
\(x^{2}\) – 9x < –18
Rewrite in standard form
x^2 -9x +18 < 0
Factorise the equation
\(x^{2}\) - 3x -6x +18 < 0
x (x - 3) - 6 (x - 3) < 0
(x - 3) ( x- 6) < 0
(x - 3) < 0
x < 3
( x- 6) < 0
x < 6
3 < X < 6
Therefore, the solution to the inequality is 3 < X < 6
Learn more about inequality equation here: https://brainly.com/question/24372553
#SPJ1
2. Suppose the price of good x increased from 4 birr to 5 birr. Because of change price of good x, quantity demand of good y changed from 5,000 to 6,250. a. Find cross price elasticity of demand b. What types of goods (good x and good y) are?
Answers
Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.
Let's calculate the cross-price elasticity of demand using the given information:
a. Find the percentage change in quantity demanded of good Y:
Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100
Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%
b. Find the percentage change in the price of good X:
Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100
Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%
Now, we can calculate the cross-price elasticity of demand:
Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X
Cross-Price Elasticity of Demand = 25% / 25% = 1
b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:
If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.
Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.
For more questions on Demand.
https://brainly.com/question/14274996
#SPJ8
Answer:
Step-by-step explanation:
Beth wants to determine a 99 percent confidence interval for the true proportion pp of high school students in the area who attend their home basketball games. Out of nn randomly selected students she finds that that exactly half attend their home basketball games. About how large would nn have to be to get a margin of error less than 0.01 for pp
Answers
Answer: 16590
Step-by-step explanation:
Let p be the population proportion of high school students in the area who attend their home basketball games.
As per given,
prior p = 0.5
Margin of error E= 0.01
Criticfor z-value for 99% confidence = 2.576
Sample size will be computed as
\(n=p(1-p)(\frac{z^*}{E})^2\\\\ n= 0.5(1-0.5)(\frac{2.576}{0.01})^2\\\\=0.25(257.6)^2\\\\=0.25 (66357.76)\approx16590\)
Hence, required sample size = 16590
3=5/(2-X), solve for x
Answers
The solution for x in the equation 3 = 5/(2 - x) is 11/3
How to determine the solution for x in the equationFrom the question, we have the following parameters that can be used in our computation:
3 = 5/(2 - x)
Cross multiply the equation
so, we have the following representation
3(2 - x) = 5
This gives
2 - x = 5/3
So, we have
x = 2 + 5/3
Evaluate the sum of the like terms
x = 11/3
Hence, the solution for x in the equation is 11/3
Read more about equation at
https://brainly.com/question/148035
#SPJ1